T. Sanders

activity

20062026

most citedOn the Bogolyubov-Ruzsa lemma

157 citations · 642 across the 35 of their papers we have counts for

collaborators

Showing math.COShow all

9 papers · 1 filter

math.CO2026

Modular Schur numbers

Tom Sanders

We study modular analogues of Schur numbers for systems of linear equations. We show that these only depend on the number of equations, not their coefficients and in the case of on…

math.CO2019★ 4 cited

Bootstrapping partition regularity of linear systems

Tom Sanders

Suppose that $A$ is a $k \times d$ matrix of integers and write $R_{A} : N \to N \cup {\infty}$ for the function taking $r$ to the largest $N$ su…

math.CO2019★ 3 cited

Schur's colouring theorem for non-commuting pairs

Tom Sanders

For G a finite non-Abelian group we write c(G) for the probability that two randomly chosen elements commute and k(G) for the largest integer such that any k(G)-colouring of G is g…

math.CO2018

The stability of finite sets in dyadic groups

Tom Sanders

We show that there is an absolute $c > 0$ such that any subset of $F_{2}^{\infty}$ of size $N$ is $O (N^{1 - c})$ -stable in the sense of Terry and Wolf. By contrast a size $N$ arit…

math.CO2018

The coset and stability rings

Tom Sanders

We show that if $G$ is a discrete Abelian group and $A \subset G$ has $∥ 1_{A} ∥_{B (G)} \leq M$ then $A$ is $O (exp (π M))$ -stable in the sense of Terry and Wolf.

math.CO2018

Almost homomorphisms between the Boolean cube and groups of prime order

Tom Sanders

We show that if f is an injection from an n-dimensional Boolean cube (considered as an additive group) to a group of prime order then the probability that f(x+y)=f(x)+f(y) is O(2^{…